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The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night.

| Stem | Leaves |
|------|-----------------|
| 0 | 9 |
| 1 | 2, 4, 7 |
| 1 | 3, 6, 6, 8 |
| 2 | 1, 2, 2, 4, 5 |
| 3 | 9 |
| 5 | |

Why is the plot misleading?

A. The plot shows that the data is skewed.
B. There is not an equal number of data points for each stem.
C. The plot shows duplicate data points.
D. The stem does not clearly show the outlier.



Answer :

GinnyAnswer
Let's analyze the stem-and-leaf plot to understand why it might be misleading:

[tex]\[ \begin{tabular}{l|lllll} 0 & 9 & & & \\ 1 & 2 & 4 & 7 & \\ 1 & 3 & 6 & 6 & 8 \\ 2 & 1 & 2 & 2 & 4 & 5 \\ 3 & 9 & & & \\ 5 & & \end{tabular} \][/tex]

1. Duplicate Data Points:
- In the plot, one of the stems under '1' has the leaf sequence `6 6`. This means the number `16` appears twice. Duplicate data can sometimes make the visualization confusing if not properly addressed, but they are generally still a part of the data.

2. Unequal Number of Data Points for Each Stem:
- If we look closely, the number of data points per stem is inconsistent. For example:
- The stem '0' has only one data point (`9`).
- The stem '1' collectively has 7 data points (`2 4 7` and `3 6 6 8`).
- The stem '2' has 5 data points (`1 2 2 4 5`).
- Stems '3' and '5' have one and zero data points respectively (`9` and no leaves).
- Such inconsistency can make the data representation unclear and difficult to interpret in terms of distribution. Ideally, for better visual comparison, each stem should have a comparable number of data points unless there are naturally large gaps in the data.

3. Outlier Detection:
- The plot currently does not have a clear indicator of outliers. In a well-constructed stem-and-leaf plot, outliers should stand out prominently. Here, the stems don't suggest any clear outliers since they are not explicitly marked or differentiated.

Given these points, we can conclude that the stem-and-leaf plot is misleading due to:

- Duplicate Data Points: There are repetitions in the dataset that are not clearly distinguished.
- Unequal Number of Data Points for Each Stem: The data points are not evenly distributed across the stems.
- Unclear Outliers: The plot does not clearly represent any outliers.

These issues collectively make the data representation in the given stem-and-leaf plot misleading.

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